Problem: Calculate the quotient below and give your answer in scientific notation. ${\dfrac{2.40\times 10^{2}}{3.0\times 10^{-1}}} =\ ?$
Start by collecting the significands and exponents. $ {\dfrac {{2.40} \times {10^{2}}} {{3.0} \times {10^{-1}}} = {\dfrac{2.40}{3.0}} \times {\dfrac{10^{2}}{10^{-1}}}} $ Then divide each term separately. When dividing exponents with the same base, subtract their powers. $= {0.80} \times {10^{2 \,-\, -1}}$ $= {0.80} \times {10^{3}}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$. In this case, we need to move the decimal one position to the right without changing the value of our answer. We can use the fact that ${0.80}$ is the same as ${8.0 \div 10}$, or ${8.0 \times 10^{-1}}$. $ = {8.0 \times 10^{-1}} \times {10^{3}} $ $ = 8.0 \times 10^{{-1} + {3}} $ $= 8.0\times 10^{2}$